Phương trình mặt câu tâm I(a,b,c) có bán kính R  là

x2+y2+z2+2ax+2by+2cz−R2=0

x2+y2+z2+2ax+2by+2cz+d=0

x2+y2+z2+2ax+2by+2cz+d=0,   d=a2+b2+c2−R2

x2+y2+z2−2ax−2by−2cz+d=0,  a2+b2+c2−d>0